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STARTING  CURRENTS  OF  TRANSFORMERS 


BY 

* 

TRYGVE   D  YENSEN 

M.  S.  University  of  Illinois,  1912 


THESIS 

Submitted  in  Partial  Fulfillment  of  the  Requirements  for  the 

Degree  of 
ELECTRICAL  ENGINEER 

IN 

THE  GRADUATE  SCHOOL 

OF  THE 

UNIVERSITY  OF  ILLINOIS 
1913 


UNIVERSITY  OF  ILLINOIS 
THE  GRADUATE  SCHOOL 


190  ') 


1  HEREBY  RECOMMEND  THAT  THE  THESIS  PREPARED  UNDER  MY  SUPERVISION  BY 


ENTITLED 


Z/ 


7 


BE   ACCEPTED    AS   FULFILLING    THIS    PART    OF    THE    REQUIREMENTS   FOR  THE 


DEGREE  OF 


rT^Gfrar^e  of  Major  Work 

^fe-y — ^ 

R|*k3  of  Department 


Recommendation  concurred  in: 


Committee 


on 


Final  Examination 


247478 


UIUC 


university  of  illinois 
Engineering  Experiment  Station 


Bulletin  No.  55  February.  1912 

STARTING  CURRENTS  OF  TRANSFORMERS 

WITH  SPECIAL  REFERENCE  TO  TRANSFORMERS 
WITH  SILICON  STEEL  CORES 

By  Trygve  D  Yensen,  Assistant,  Electrical  Engineering  Department,  Engineering 

Experiment  Station 

CONTENTS 
I.  Introduction 

PAGE 

1.  Preliminary    3 

2.  Acknowledgments    3 

3.  Theory    3 

4.  Method  of  Investigation    7 

II.  (a)   Actual  Measurements  of  Phenomena  by  Means  of 

Oscillograms 

=5.    Connections    8 

6.  Transformers    8 

7.  Residual  Magnetism   9 

8.  Oscillograms    10 

II.  (b)  Theoretical  Calculations  from  Transformer  Data 

9.  Magnetization  Curves  and  Hysteresis  Loop   12 

10.  Calculations    15 

11.  Agreement  between  Oscillograms  and  Calculations   23 

III.  Calculations  of  Maximum  Starting  Current  for 

Various  Types    23 

IV.  Effect  of  Resistance  and  Inductance  in  Series 

with  Transformer  Primary   34 

V.    Summary  and  Conclusions   38 

Appendix    41 


STARTING  CURRENTS  OF  TRANSFORMERS 

WITH   SPECIAL  REFERENCE  TO  TRANSFORMERS 
WITH  SILICON  STEEL  CORES 


I.  Introduction 

1.  Preliminary. — It  is  generally  known  that,  in  closing  the 
primary  circuit  of  a  transformer,  a  transient  effect  may  take  place  in 
the  form  of  a  momentary  rush  of  current,  due  to  the  residual  magnet- 
ism of  the  transformer  iron.  With  the  introduction  of  the  new  silicon 
steel  for  transformer  cores,  with  the  resulting  increase  in  flux  densities, 
this  transient  effect  has  been  materially  magnified,  and  may,  in  some 
cases,  reach  dangerous  proportions. 

It  is  the  object  of  this  bulletin  to  present  some  facts  with  regard  to 
this  phenomenon,  obtained  by  means  of  commercial  apparatus,  and  to 
show  how  to  protect  the  system  from  injury  due  to  this  cause. 

2.  Acknowledgments. — Valuable  assistance  in  the  preparation  of 
the  oscillograms  has  been  rendered  by  Messrs.  C.  E.  Bennett  and  A.  C. 
Hobble,  of  the  Electrical  Engineering  Department. 

3.  Theory. 

(a)  Inductance  without  Iron. — If  an  alternating  e.  m.  f. 
e  =  £max  sin  0,  be  impressed  upon  a  circuit  containing  resistance  and  in- 
ductance without  iron,  in  series,  this  impressed  e.  m.  f .  will  be  consumed 
by  the  counter  e.  m.  f .  of  the  inductance,  and  by  the  drop  through  the 
resistance,  and  this  must  be  true  at  every  instant,  i.  e.,  for  every  point 
of  the  impressed  e.  m.  f.  wave.    We  have,  therefore, 

,  =  £raaxsin0  =  L  d±  +Ri  (1) 


where 
Since 


and 


max dt 
0  is  the  phase  angle  of  the  impressed  e.  m.  f.  =  2tt  ft. 
di     di  dO     di  , 

Jt=Jo  dt  =  Je2ir' 

L  —  =  2  7T  fL  ~  =  X         where  X   =  inductive  reactance 
dt  d6         L  d0 

di 

£max  sin  0  d  0  =  Xl  di  +  Rid  0 


-£max(f  (cos0)=XL  di  +  RidO 


4  ILLINOIS  ENGINEERING  EXPERIMENT  STATION 

di  =  (cos  6)—£-  id  6  (2) 

If  the  circuit  be  closed  at  that  point  of  the  e.  m.  f.  wave  where 
<?==£max>  i-  e.,  when  B  =  900  =  -  ,  and  if  the  resistance  drop  be 

assumed  negligible,  (2)  becomes 

E 

di  =  d  (cos  6)  (3) 

L 

If  the  circuit  be  closed  at  different  points  of  the  e.  m.  f.  wave,  the 
current  will  rise  to  different  values,  and  these  values  can  now  readily 
be  investigated  by  means  of  the  last  equation. 

Suppose  for  instance,  that  we  close  the  circuit  at  the  900  point  of 
the  e.  m.  f.  wave,  i.  e.,  when  the  e.  m.  f.  is  a  maximum. 
Integrating  (3)  from  tt/2  to  tt 


j  di  =  —  ^r*J  d  (cos  6) 


X 


which  is  the  maximum  current  reached,  since  integrating  from  -  to 
ir  +  a,  where  a  is  a  constant,  less  than  2  w,  results  in  a  value  less  than 

■^max 

showing  that  the  current  decreases  from  this  point. 

Suppose,  in  the  next  case,  that  the  circuit  be  closed  at  the  o° 
point  of  the  e.  m.  f .  wave,  i.  e.,  when  e  =  o  and  6  =  o. 

Integrating  (3)  from  o  to  -  gives 


P  E  P 

J.*=- :?J. 


d  (cos  6) 


E 

max 


X. 


the  same  as  before. 
Integrating  from  o  to  ir,  however, 

i.  e.,  the  maximum  current  obtained  in  this  case  is  twice  that  obtained 
when  the  circuit  is  closed  at  the  900  point  of  the  e.  m.  f .  wave. 

In  a  similar  way  it  can  be  shown  that  by  closing  the  circuit  at  any 
other  point  of  the  e.  m.  f.  wave,  the  maximum  current  reached  will  lie 


d  (cos  6)  =  +  2 

X, 


YICNSKN — STARTINC   (  I '  UKI'.NTS  OF   TKAN'Sl'OKM  KKS 


5 


between 


and  2^ix 


In  general,  the  current  assumes  its  normal  value  only  when  the 
circuit  is  closed  at  that  point  of  the  impressed  e.  m.  f.  wave,  where 
the  permanent  value  of  the  current  is  zero.  In  the  above  case,  where 
there  is  negligible  resistance,  this  is  the  900  point  of  the  wave.  The 
effect  of  the  resistance  is  to  move  this  point  towards  the  zero  point. 

(b)  Inductance  ivith  Iron. — The  above  calculations  assume  a 
constant  inductance,  i.  e.,  a  straight  line  magnetization  curve,  obtained 
by  using  an  inductance  without  magnetic  material  as  core.  If  an  iron 
core  be  employed,  such  as  is  the  case  with  the  ordinary  induction  coil 
or  the  transformer,  the  inductance  is  not  constant.  As  the  flux 
density  increases,  the  inductance  decreases,  until  the  iron  is  perfectly 
saturated.  After  this  point  is  reached,  the  inductance  remains  constant 
at  a  small  value,  depending  only  upon  the  flux  passing  between  the 
coil  and  the  core  through  the  air  or  non-magnetic  material. 

Since  the  flux  is  not  any  longer  proportional  to  the  current,  the 
counter  e.  m.  f.  due  to  the  inductance  must  be  written 

AdB 

Ade 

where  B  =  flux  density  and  A  =  constant, 
instead  of 

,  di  di 
L-r  or  X  -r- 
dt         L  dd 

and  equation  (1)  becomes 

e=Em3Xsmd  =  A^-  +  Ri  (4) 

—  £n„x  d  (cos  9)  =  AdB  +  Rid  0 

dB  =  —  ^d(cosO)—  ^-idd  (5) 

Under  normal  conditions,  the  resistance  drop  due  to  the  magnetizing 
current  of  a  transformer  is  negligible,  and 

dB  =  ^  d  (cos  6) 
The  normal  maximum  value  of  B  is  then  obtained  by  integrating  dB 

IT 


from   -  to  7r. 
2 


J, 


dB  =  B     =—  E 

max  max 


cos 


1  ^  =  £m^x 
A 


6 


ILLINOIS  ENGINEERING  EXPERIMENT  STATION 


.\^  =  £maxand^=!^  (6) 

max 

Substituting  (6)  in  (5) 

dB  Bmd  (cosd)—  §®*Rid6   (7) 

max 

Since  the  relation  between  the  magnetizing  current  and  the 
resulting  flux  can  not  be  expressed  mathematically  in  any  practical 
equation,  the  magnetizing  current  necessary  to  produce  the  required 
flux  according  to  the  above  equation  can  be  determined  only  analyt- 
ically, as  follows : 


Fig.  1 


Suppose  Fig.  1  to  represent  the  saturation  curve  of  a  transformer 
and  the  hysteresis  loop  for  normal  voltage  and  frequency.  The  hys- 
teresis loop  shows  what  residual  magnetism  remains  in  the  iron  after 
the  current  has  been  removed,  ob  and  od  represent  this  residual 
magnetism,  depending  upon  whether  the  current  has  died  down  from  a 
positive  or  a  negative  value. 

Suppose  the  circuit  is  closed  when  the  impressed  e.  m.  f.  passes 
through  0  from  negative  to  positive,  i.  e.,  8  =  0,  and  that  the  residual 
magnetism  is  ob.  It  is  evident  then  that  the  change  of  flux  to  pro- 
duce the  counter  e.  m.  f.  must  start  from  b.  If  equation  (7)  be  re- 
written in  the  form 

*£  =  -£maxA(cos0)  -  p^Ri^e  ......(8) 

max 

and  small  intervals  of  6,  say  io°,  be  taken,  the  actual  conditions  can 
very  nearly  be  approached.  Starting  from  b,  the  flux  will  follow  a 
curve,  such  as  the  dashed  curve  between  b  and  a,  and  will  continue  on 
the  saturation  curve.    From  equation  (8),  A  B  can  be  calculated  for 


YENSEN — STARTING  CURRENTS  OF  TRANSFORMERS 


7 


each  increment  of  io°,  starting  from  0°  in  this  case,  and  from  Fig.  i 
can  be  obtained  the  corresponding  magnetizing  current  required  to 
produce  the  total  flux,  Bi  -f  AB,  Bi  being  the  total  flux  at  the  beginning 
of  the  interval.  After  having  determined  the  magnetizing  current,  the 
resistance  drop  effect  is  calculated,  equal  to 

jf*  Ri  A  6  (9) 

This  will,  however,  reduce  the  value  of  A  B,  and  a  few  trials  will  have 
to  be  made  before  the  correct  value  of  A  B  is  found. 

Proceeding  in  this  manner,  the  flux  and  the  corresponding  mag- 
netizing current  may  be  determined  for  any  number  of  cycles.  For 
decreasing  values  of  flux,  the  upper  dashed  curve  in  Fig.  i  has  to  be 
used.  It  will  be  found  that  the  magnetizing  current  may  reach  for- 
midable values  under  unfavorable  conditions,  particularly  for  the  first 
cycle.  The  amplitude  of  the  peaks  decreases  rapidly,  the  more  so  the 
larger  the  amplitude  of  the  first  peak,  on  account  of  the  more  pro- 
nounced effect  of  the  resistance  in  that  case. 

4.  Method  of  Investigation. — In  Part  II  (a)  will  be  taken  up 
the  actual  measurements  of  the  magnetizing  current  of  a  transformer 
upon  closing  the  primary  circuit  at  a  predetermined  point  of  the  e.  m.  f. 
wave,  and  with  a  known  residual  magnetism  in  the  iron.  These  meas- 
urements were  made  by  means  of  oscillograms,  showing  the  impressed 
e.  m.  f.,  the  primary  magnetizing  current,  and  the  secondary  induced 
e.  m.  f. 

Part  II  (b)  takes  up  the  calculations  of  the  flux  and  magnetizing 
current  for  the  conditions  under  which  the  oscillograms  were  taken. 
In  order  to  do  this,  all  the  characteristics  of  the  circuit  and  transformer 
having  any  bearing  upon  the  magnetizing  current  were  carefully  ob- 
tained. The  curves  plotted  show  that  there  is  very  close  agreement 
between  the  actual  curves,  as  obtained  by  means  of  the  oscillograms, 
and  the  calculated  curves  as  obtained  by  means  of  the  circuit  and 
transformer  characteristics.  This  agreement  shows  that  it  is  possible 
to  make  calculations  of  these  phenomena,  that  can  be  fully  relied  upon, 
and  that  it  is  unnecessary  to  resort  to  the  oscillograph  in  order  to 
obtain  reliable  results.  It  was  therefore  deemed  sufficient  for  the 
investigation  of  the  rest  of  the  transformers,  covered  by  this  bulletin, 
to  obtain  the  transformer  data  necessary  to  make  the  calculations 
as  shown  in  Part  III.  These  calculations  cover  the  most  critical  condi- 
tion only,  namely,  the  rush  of  current  upon  closing  the  circuit  at  the  o° 
point  of  the  e.  m.  f.  wave  with  the  residual  magnetism  in  the  same 
direction  in  which  the  increase  of  flux  will  take  place  upon  closing 
the  circuit. 


8 


ILLINOIS  ENGINEERING  EXPERIMENT  STATION 


In  I  art  IV,  is  given  the  result  of  placing  a  resistance  or  air  core 
inductance  in  series  with  the  transformer,  and  it  is  shown  how  to  cal- 
culate a  resistance  or  inductance  sufficient  to  limit  the  rush  of  current 
to  safe  values. 


II. 


(a)   Actual  Measurements  of  Phenomena  by  Means  of 
Oscillograms. 


5.  Connections.— Fig.  2  is  a  diagram  of  the  connections  used  for 
obtaining  the  oscillograms.  G  is  a  10  kw.  440-v.  alternator,  60  cycles 
with  taps,  so  as  to  give  either  3-phase  or  2-phase  current,  as  shown  in 
Fig.  2a  Taps  1,  3  and  5  are  used  for  3-phase,  taps  1-4,  2-6,  for  2-phase. 
the  closing  switch  was  designed  and  built  specially  for  the  investiga- 
tion of  these  phenomena.1  It  was  attached  to  the  end  of  the  generator 


C/osiny  Smtch} 


i  r 


/Cow  Afon  /nduct'w 

fes/stance-  Transformer 


/v\tvw-@-T 


Fig. 


j  Osci/oarapfj 


4 

Fig.  2a 

shaft,  and  can  be  set  so  as  to  close  the  circuit  at  any  predetermined 
point  of  the  e.  m.  f.  wave.  However,  it  would  not  operate  satisfactorily 
at  the  normal  speed  of  the  generator,  1800  r.  p.  m.  A  speed  of  650 
r.  p.  m.  was  finally  decided  upon,  which  resulted  in  a  frequency  of  22 
cycles. 

6.  Transformer.— A  5-kw.  60  cycles  2200,  1100/220,  no-volt 
transformer  of  the  newest  type  was  used  in  this  test.  It  was  connected 
for  no  volts  primary,  i.  e.,  with  the  low  tension  coils  in  parallel.  As 
the  normal  frequency  is  60  cycles,  and  22  cycles  was  used,  the  voltage 

JBy  O.  B.  Wooten,  Research  Fellow,  Engineering  Experiment  Station. 


YENSEN — STARTING  CURRENTS  OF  TRANSFORMERS 


9 


had  to  be  reduced  in  proportion,  i.  e.,  the  impressed  voltage  was 

22 

II0^6o  =  4°  v°lts>  to  give  normal  magnetizing  current. 

As  it  was  desirable  to  use  as  stiff  a  field  as  possible  in  the  gener- 
ator, in  order  to  prevent  too  much  of  a  voltage  drop  upon  closing  the 
transformer  circuit,  taps  2-3,  (Fig.  2a),  were  used,  giving  40  volts  with 
about  full  field  and  650  r.  p.  m.  The  oscillograms  show  that  the  voltage 
is  kept  up  fairly  well  at  the  maximum  rush  of  current. 

7.  Residual  Magnetism. — The  normal  magnetizing  current  was  ob- 
tained by  impressing  110  volts  at  60  cycles  upon  the  transformer.  The 
result  is  shown  in  the  following  table. 


Table  i 

Volts  Current  Watts  Freq. 

E  7CX  W  F 

no  .90  46.5  60 


The  maximum  value  of  the  exciting  current  =  .90  X  V  2  =  1.27  am- 
peres, and  this  is  the  current  that  produces  the  normal  residual  mag- 
netism. 

A  series  of  experiments  was  made  to  ascertain  the  decrease  of 
the  residual  magnetism  after  the  removal  of  the  e.  m.  f.  These 
experiments  are  described  in  the  Appendix.  The  following  results 
were  obtained : 

1.  There  is  no  decrease  in  the  residual  magnetism  of  transform- 
ers under  normal  conditions. 

2.  The  decrease  of  residual  magnetism  due  to  vibration  or  shock 
is  very  small,  almost  negligible. 

The  oscillograms  were  taken  with  a  residual  magnetism  in  the  iron 
that  would  remain  after  the  removal  of  the  normal  voltage  at  normal 
frequency,  which  would  be  the  case  under  normal  operating  con- 
ditions. 

This  residual  magnetism  was  produced  by  means  of  direct  current 
from  a  storage  battery,  as  shown  in  Fig.  2.  The  current  used  was  that 
corresponding  to  the  normal  exciting  current  of  the  transformer,  the 
maximum  value  of  which  is  1.27  amp.  Hence  1.27  amp.  D.  C.  was 
used. 

By  means  of  a  reversing  switch,  S2,  the  current  could  be  reversed, 
producing  a  residual  magnetism  in  the  opposite  direction.  In  order  to 
be  sure  that  the  correct  residual  magnetism  was  produced,  the  iron  was 
sent  through  the  regular  hysteresis  loop  a  number  of  times,  at  least 


o 


S  >  s 

«  S 


10 


ILLINOIS  ENGINEERING  EXPERIMENT  STATION 


ten,  by  reversing  the  current  by  means  of  switch  S.,.  Let  Fig.  3  rep- 
resent the  normal  hysteresis  loop.  Suppose  the  residual  magnetism,  at 
the  beginning,  is  at  2'.  Sending  -j-/m  amperes  through  the  transformer 
increases  the  magnetism  to  i'  along  the  lower  dashed  curve.  Opening 
the  switch  decreases  the  magnetism  to  2'.  Reversing  the  switch  brings  it 
near  3.  Again  opening  the  switch  brings  it  near  4.  Going  through 
the  same  operations,  the  loop  will  approach  1-2-3-4  and,  after  a  few 
reversals,  practically  coincide  with  it.  so  that  when  the  switch  is  finally 
opened,  the  residual  magnetism  will  be  0-2  or  0-4,  according  to  whether 
the  last  current  was  -f-  Im  or  —  /m. 


Fig  3 

8.    The  Oscillograms. — Out  of  a  total  number  of  eleven  oscillo- 
grams taken,  four  are  here  reproduced,  as  follows: 
Oscil.  7.  Circuit  closed  at  o°  point  of  e.  m.  f.  wave. 
Residual  magnetism,  positive. 
Maximum  rush  of  current  =52.1  amp. 
Oscil.  9.  Circuit  closed  at  900   point    (more   accurately  850  point) 
of  e.  m.  f.  wave. 
Residual  magnetism,  positive. 
Maximum  rush  of  current  =  18.0  amp. 
Oscil.  8  (a)*  Circuit  closed  at  o°  point  of  e.  m.  f.  wave. 
Residual  magnetism,  negative. 
Maximum  rush  of  current  =  3.78  amp. 


12 


ILLINOIS  ENGINEERING  EXPERIMENT  STATION 


8  (b)*    Same  conditions. 

Maximum  rush  of  current,  unknown. 
Oscil.  4.    Circuit  closed  at  o°  point  of  e.  m.  f.  wave. 
Residual  magnetism,  uncertain. 
Maximum  rush  of  current  =  32.0  amp. 
By  positive  residual  magnetism  is  meant  that  the  magnetism  was  in  the 
same  direction  in  which  the  flux  would  increase  upon  closing  the 
circuit. 

II.  (6)  Theoretical  Calculations  from  Transformer  Data. 

9.  Magnetization  Curves  and  Hysteresis  Loop. — These  were  ob- 
tained in  the  following  way.  The  transformer  was  connected  as  shown 
in  Fig.  4.   Direct  current  from  a  storage  battery  was  supplied  the  high 


Fig.  4 

tension  side  P  of  the  transformer  through  a  reversing  switch,  S,  and 
a  resistance  Rp.  The  low  tension  side  was  connected  to  a  high  resist- 
ance R,  and  a  D'Arsonval  galvanometer,  connected  across  a  small  part 
of  the  resistance,  with  a  very  high  resistance  in  series.  A  change  of 
flux  in  the  transformer  would  then  produce  a  deflection  of  the  galvano- 
meter coil,  proportional  to  the  total  change  of  flux.  R,  Rs  and  r  were 
not  changed  during  the  experiment,  so  that  the  deflections  obtained,  mul- 
tiplied by  a  constant  K,  gave  the  flux  density  in  the  transformer  core. 
In  this  investigation,  the  absolute  flux  density  in  gausses  was  not  cal- 
culated, as  it  is  only  the  relative  flux  values  that  are  needed.  The  flux 
density  is  therefore,  throughout  this  bulletin,  expressed  as  a  galvano- 
meter deflection  multiplied  by  a  constant,  K,  Ku  K2,  etc.  for  different 
transformers. 

To  obtain  the  curves,  the  desired  current  was  sent  through  the 
transformer  primary,  reversed  a  number  of  times  to  be  sure  that  the 
iron  had  entered  the  corresponding  loop,  and  the  current  left  on  in  the 

*Note.  Two  exposures  were  made  on  Oscil.  8:  8  (a)  in  which  the  cur- 
rent only  appeared;  8  (b)  containing  all  quantities.  The  two  exposures  have 
been  traced  separately. 


VKNSEN — STARTING  CURRENTS  OF  TRANSFORMERS 


13 


I 


Fig.  5.   Magnetization  Curve  and  Hysteresis  Loop  for  Transformer  A. 


ILLINOIS  ENGINEERING  EXPERIMENT  STATION 


positive  direction,  corresponding  to  point  i  in  Fig.  3.  The  galvano- 
meter was  then  connected.  Opening  the  circuit,  the  resulting  deflection 
corresponded  to  a  change  of  flux  1-2,  reversing  the  current  produced 
a  change  2-3 ;  opening  it  produced  a  change  3-4 ;  again  reversing  it  pro- 
duced a  change  4-1,  completing  the  loop. 

Fig.  5  shows  the  hysteresis  loop  and  magnetization  curves  for  the 
transformer  used  for  the  oscillograms.  It  was  obtained  by  the  method 
explained  above.  As  an  example,  is  given  the  galvanometer  deflec- 
tions for  1.22  amp. 


Table  2 


Current 


1 .22 


Change 

Deflection 

=  A<f>  X  K 

1-2 

9-5 

59-5 

2-3 

50.0 

2 

3-4 

9-5 

59-5 

4-i 

50.0 

2 

=  29.75 
=  29.75 


Resid.  Mag. 

29-75  —  9-5 
=  20.25 


The  saturation  curve  was  carried  up  to  119  amp.  It  is  seen  that 
at  this  point  the  curve  has  become  a  straight  line,  which  means  that  the 
iron  has  become  saturated,  and  the  increase  in  flux  is  taking  place 
only  in  the  non-magnetic  space  between  the  iron  and  coil.  Conse- 
quently, the  curve  can  be  extended  indefinitely. 


O'  90'  /80°         270'         760°         -450°  S40'  630' 

Fig.  6.  Rush  of  Current  on  Closing  the  Primary  Circuit  of  Transformer  A. 
Circuit  closed  at  o°  point  of  e.  m.  f .  wave.    Residual  magnetism  =  +  20  X  K. 


YENSEN  STARTING  CURRENTS  OF  TRANSFORMERS 


15 


9.  Calculations.— The  data  needed  for  the  calculations  of  the 
magnetizing  current  are  as  follows  : 
1.    Normal  hysteresis  loop; 

2     Magnetization  curve  up  to  straight  line  relation ; 

3.  Total  effective  voltage  impressed  upon  the  transformer  circuit; 

4.  Total  resistance  of  circuit ; 

5.  Total  inductance  of  circuit. 

Sine  wave  e.  m.  f.  is  assumed  in  these  calculations.  Equation  (8), 
gives  the  relation : 

.(8) 


AS  =  -BmaxA(cos0)-|^/vtA0 


assuming  the  circuit  to  have  negligible  inductance  outside  the  trans- 
former. 


i80'         eTO'         36  O'        45-0°  S40° 

Fig.  7.  Rush  of  Current  on  Closing  the  Primary  Circuit  of  Transformer  A. 
Circuit  closed  at  85°  of  e.  m.  f .  wave.    Residual  magnetism  equals  +2oX£ 


l6  ILLINOIS  ENGINEERING  EXPERIMENT  STATION 

B  =  flux,  Bmnx  =  max.  flux  of  normal  hysteresis  loop ; 

£m«x  =  »1'i^-  impressed  e.  m.  f.  =  y2£eff; 

R  =  total  resistance  of  circuit ; 

t  =  instantaneous  value  of  magnetizing  current. 

In  the  present  case, 

5maX  (from  Fig.  5)  =  29.5  X  K,  where  K  =  const. 

Eac  =  40  volts.    £mix  =  yj2  X  40  =  56.5  volts. 

R  =  .745  ohms. 

Substituting  in  (8),  for  increments  of  8  of  io°,  i.  e.  A  6  =  ioc 
radians, 

A  B  =  —  29.5  K  A  (cos  6)  —  .0685  K  i. 


•175 


14 


so 

\  * 

X  8\4o 


—  c 

l/CL 

Cut 

-re/ 

if 

/ 

a/c 

j/a 

r. 

'i/X 

« — 

/ 

/ 

\ 

/ 

\ 

\ 

/ 

/ 

\ 

/ 

1 — 

\ 

/ 

H— 

 V 

\ 

 1 — 

/ 

— V 

\ 

1 

\ 

~r 
I 

\ 

-\- 

1 

r 

-V- 
\ 

h 

\ 

1 

\ 

\ 

-V- 

~t 
-J- 

\ 

\ 

-v- 

x~~ 

/ 

/ 

/ 

-\ 

v.. 

/ 

90°  /So'         270'         360'         4S0°         &4o'  €SO' 

Fig.  8.  Rush  of  Current  on  Closing  the  Primary  Circuit  of  Transformer  A. 
Circuit  closed  at  90°  point  of  e.  m.   f.  wave.     Residual  magnetism  equals 

+  20  X  if 


YEN  SEN — STARTING  (  URRENTS  OF  TRANSFORM  ICRS  IJ 

In  Table  3  arc  given  the  calculations  for  a  number  of  different 
conditions,  viz.. 


Conditions 


Closing 

Point 
on  e.  m.  f. 

wave 

Residual 
Magnetism 

Impressed 
e.  ra.  f .  , , 

ef  1 

Frequency    Resist,  of 
Cycles/Sec  Circuit 

Columns   4  to  7 
Columns   8  to  11 
Columns  12  to  15 
Columns  16  to  19 
Columns  20  to  23 

0° 

85° 
90° 
0° 
90° 

+  20  K 
4-  20  K 
+  20  K 

—  20  K 

—  20  K 

40  volts 
40  volts 
40  volts 
40  volts 
40  volts 

22  .745 
22  .745 
22  .745 
22  .745 
•  745 

These  conditions  correspond  to  those  under  which  the  oscillograms 
were  taken. 


Of  90'  /80°  270'         360'        4S0'         540'  €30' 


Fig.  9.  Rush  of  Current  on  Closing  the  Primary  Circuit  of  Transformer  A. 
Circuit  closed  at  0°  point  of  the  e.  m.  f.  wave.    Residual  magnetism  equals 

—  20  X  if.  * 


[8 


ILLINOIS  LNGIN  LICKING  LXPERIMLNT  STATION 


^-/2  -60 


90' 


/80' 


630' 


e70°  T60'  450'  S40' 

Fig.  io.  Rush  of  Current  on  Closing  the  Primary  Circuit  of  Transformer  A. 
Circuit  closed  at  go"  point  of  the  e.  m.  f.  wave.  Residual  magnetism  = —  20  X  K. 

In  Fig.  11  are  plotted  the  calculated  values  of  current,  flux  and 
impressed  e.  m.  f.  for  the  various  conditions,  to  the  same  scale,  in 
order  to  compare  readily  the  effect  of  the  closing  point  and  the  resi- 
dual magnetism.  Fig.  11  is  a  summary  of  Fig.  6  to  10  inclusive  and 
Table  3. 

11a  corresponds  to  Table  3,  Columns  4-7,  and  Fig.  6. 
11b  corresponds  to  Table  3,  Columns  12-15,  and  Fig.  8. 
lie  corresponds  to  Table  3,  Columns  16-19,  and  Fig.  9. 
ud  corresponds  to  Table  3,  Columns  20-23,  and  Fig.  10. 

lie  represents  the  condition  in  which  the  circuit  is  closed  at  the 
900  point  of  the  e.  m.  f.  wave  with  no  residual  magnetism.  This  is  the 
condition  for  normal  closing,  since  the  flux  and  current  then  will  enter 
at  once  upon  their  normal  path.  The  same  result  would  be  obtained 
under  conditions  of  Fig.  no.  if  the  initial  magnetism  were  negative 
maximum;  under  conditions  in  Fig.  lib,  if  the  initial  magnetism  were 
o;  under  conditions  of  Fig.  11c,  if  the  initial  magnetism  were  negative 
maximum,  and  under  conditions  of  Fig.  ud  \i  the  initial  magnetism 
were  o.  It  is  seen  that  the  closer  the  conditions  come  to  these  normal 


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YENSEN — STARTING  CURRENTS  0E  TRANSFORMERS 


23 


conditions,  the  less  rush  of  current  takes  place.  Fig.  11c  comes  very 
close  to  these  normal  conditions,  while  Fig.  lia  is  farthest  away.  Fig. 
11b  and  d  are  practically  identical,  with  the  exception  that  in  Fig.  11& 
the  rush  of  current  is  positive,  while  in  Fig.  lid  it  is  negative. 

10.  Agreement  between  Oscillograms  and  Calculated  Curves. — 
The  values  of  flux  and  current  from  Table  3  have  been  plotted  in  Fig. 
6  to  10  inclusive,  together  with  the  actual  currents,  as  given  by  the 
oscillograms.  The  full  lines  give  the  calculated  currents.  The  dashed 
lines  give  the  calculated  flux.   The  dotted  lines  give  the  actual  currents. 

From  these  plates  it  may  be  seen  that  the  agreement  between 
the  actual  curves  and  the  calculated  curves  is  very  close.  Indeed,  for 
the  first  case,  corresponding  to  Oscil.  7  and  Table  3,  Columns  4-7, 
the  two  current  curves  practically  coincide.  For  the  second  case,  cor- 
responding to  Oscil.  9  and  Table  3,  Columns  12-15,  the  maximum  dis- 
agreement is  only  4.5  per  cent,  while  in  the  third  case,  corresponding 
to  Oscil.  8a  and  Table  3,  Columns  16-19,  the  disagreement  is  25  per 
cent. 

The  closer  agreement  in  the  first  case  was  to  be  expected,  con- 
sidering that  a  small  variation  in  the  residual  magnetism  in  Oscil.  8 
would  have  a  greater  effect  than  in  Oscil.  7,  on  account  of  the  dampen- 
ing effect  of  the  resistance  in  7,  while  the  resistance  has  practically  no 
effect  in  8.  While  the  attempt  was  made  to  have  the  residual  magnetism 
constant  in  all  cases,  it  is  possible  that  it  may  have  varied  a  small 
amount.  Assume,  for  instance,  that  the  residual  magnetism  for  Oscil. 
8  was  —  18.0  K  instead  of  —  20  K,  the  maximum  positive  flux  would 
be  approximately  37.8  -f  2.0  =  39.8  K  corresponding  to  a  current  of 
3.75  amp.  (instead  of  2.8  amp.)  which  is  the  current  shown  by  the 
oscillogram. 

However,  the  agreement  between  the  oscillograms  and  the  calcula- 
tions is  such  as  to  warrant  the  conclusion  that  reliable  results  of  the 
starting  current  of  transformers  can  be  obtained  by  calculations,  if  the 
complete  data  of  the  transformer  and  circuits  are  at  hand,  as  tabulated 
on  p.  15. 

III.   Calculation  of  Maximum  Starting  Current  of  Trans- 
formers of  Various  Types  and  Makes. 

In  the  preceding  section,  have  been  given  the  starting  currents 
of  a  no-volt  60-cycles  transformer  by  impressing  upon  it  40  volts  at 
22  cycles.  While  this  resulted  in  normal  magnetizing  currents  under 
normal  operating  conditions,  the  percentage  of  resistance  drop  in 


24 


ILLINOIS   KNOINKKKINC   KXPKRI  M  I'.NT  STATION 


terms  of  total  impressed  e.  m.  f.  is  much  greater  for  the  same  current 
than  if  1 10  volts  were  impressed. 

For  no  volts,  60  cycles,  equation  (8)  takes  the  following  form: 
(the  resistance  of  the  circuit  remaining  .745  ohms) 

29.  e  K 

A  B  =  —  29.5  K  A  (cos  6)  —  — ~—  Ri  A  6 

IIO  ^2 

A  B  =  —  29.5  K  A  (cos  6)  —  .025  Ki 

which  shows  that  the  effect  of  the  resistance  in  decreasing  A  B,  and 
consequently  the  current,  is  decreased  by  1 10/40,  or  in  proportion  to 
the  voltage. 

In  this  section,  calculations  are  given  for  the  case  in  which  the 
transformers  are  connected  directly  to  constant  potential  busbars 
with  sufficient  power  behind  to  maintain  the  voltage  constant  in  spite 
of  large  starting  currents.  The  potential  in  this  case  is  the  normal 
voltage  of  the  transformers,  and  the  resistance  of  the  leads  is  assumed 
negligible. 

The  following  transformers  have  been  treated: 


Capacity 

VOLTS 

Year  of 

Designation 

K.V.A. 

Primary 

Secondary 

Freq. 

Make 

Mfg. 

Remarks 

Transformer  A 

5 

2200/ 1 100 

220/110 

60 

X 

1910 

Same 

transfor- 

mer as 

was  used 

in  obtain- 

ing oscil- 

Transformer B 

lograms. 

5 

2080/1040 

460/230 

60 

X 

Old 

Transformer  C 

Type 

50 

?200/lI00 

440/220 

60 

Y 

1910 

Transformer  D 

440 

no 

60 

Y 

Old 

Transformer  E 

Type 

IS 

440/220 

220/110 

60 

Z 

1911 

The  transformers  will  now  be  taken  up  in  order,  and  the  current 
calculated  for  the  case  where  the  circuit  is  closed  at  the  o°  point  of 
the  e.  m.  f.  wave,  with  the  residual  magnetism  positive,  i.  e.,  for  the 
conditions  of  Oscil.  7,  which  give  the  maximum  rush  of  current. 


Transformer  A 

5-kw.,  2200,  1100/220,  no  volts,  60  cycles,  new  type, 
no-volt  winding  used  as  primary. 


YKNSKN — START  I  NT.  C  I'RRKNTS  OF   TRANSFORM  I'.KS 


25 


Data 

Hysteresis  loop  and  magnetization  curve  are  given  in 
F'g-  5- 

Normal  effective  voltage  =  no  volts. 
Resistance  of  circuit  =  resistance  of  transformer  = 
.0253  ohms. 

Maximum  value  of  normal  exciting  current  =1.27 
amp. 

Hence  equation  (8)  becomes 

A  B  =  —  29.5  K  A  (cos  6)  —  .00084  Ki. 

Table  4  gives  the  calculations  for  this  and  the  following  cases  from  o 
to  2000.   For  transformer  A.  it  gives  a  maximum  current  of  390  amp., 

while  the  maximum  value  of  the  full  load  current  is  only  J 2  X45  = 
64.3  amp.,  i.  e.,  the  maximum  rush  of  current  is  6.1  times  normal 
full  load. 

Transformer  B 

5-kw.  2080,  1040/460,  230  V.,  60  cycles,  old  type,  2080- 
volt  winding  used  as  primary. 

Data 

Hysteresis  loop  and  magnetization  curve  are  given  in 
Fig.  12. 

Normal  eft',  e.  m.  f .  =  2080  volts. 
Resistance   of   transf.    (2080-volt   winding)  =  9.35 
ohms. 

Maximum  value  of  normal  exciting  current  =  0.1 
amp. 

From  Fig.  12 

#max  =  26.25 

Normal  residual  magnetism  =  20.0  X  K4. 

£ms  =  y]*  X  2080  =  2940. 
Equation  (8)  becomes 

A  B  =  —  26.25  X  KiA  (cos  0)  —  .0146  KJ. 
From  Table  4,  Columns  8-1  r,  the  maximum  current  is  13.5  amp.  or 
about  4  times  the   maximum  value  of  the  full  load  current,  viz., 
V  2  X  2.4  =  3.4  amp. 

Transformer  C 

50  kw.  2200,  1 100/440,  220  volts,  60  cycles,  new  type, 
2200-volt  side  used  as  primary. 


JO 


ILLINOIS  ENGINEERING  EXPERIMENT  STATION 


-0/  0  0./         02  03  0.4  0.5 


Fig  12.    Magnetization  Curve  and  Hysteresis  Loop  of  Transformer  B. 


YENSEN — STARTING  CURRENTS  OF  TRANSFORMERS 


27 


Data 


From  Fig.  13 


Hysteresis  loop  and  magnetization  curve  are  given  in 
Fig.  13- 

Normal  eff.  e.  m.  f.  =  2200  volts. 

Resistance  of  transformer  (2200-volt  winding)  =  .446 
ohms. 

Maximum  value  of  normal  exciting  current  =  .5  amp. 


/ 

/ 



/ 

/ 

s 

* 

0 

/ 

too 



200 

s 

J00 

—- 

— — 

es 

60 

80 

*^  s  / 

// 

1 

rf 

1 

1 

1 

1 

//Of? 

0O/=> 

/ 

1  \ 

-as 


Fig.  13.   Magnetization  Curve  and  Hysteresis  Loop  for  Transformer  C. 


ILLINOIS  ENGINEERING  EXPERIMENT  STATION 


fim,x  =  2075 

Normal  residual  magnetism  =  15.25  A'., 

^max  =  yj?  X  2200  =  31  10  VOltS 

Equation  (8)  becomes 

A  B  =  —  20.75  ^2  A  (cos  ^)  —  -00052  K„  i 

From  Table  4,  Columns  12-15,  the  maximum  current  is  235  amp.  or 
about  7.3  times  the  maximum  value  of  the  normal  full  load  current, 
viz.,  J2X  22.7  =  32.1  amp. 


-/  0  /  2  j  4  s 

Fig.  14.    Magnetization  Curve  and  Hysteresis  Loop  for  Transformer  D. 


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32  ILLINOIS  ENGINEERING  EXPERIM  KNT  STATION 

Transformer  D 

7^2-kw.  440/110  volts,  60  cycles,  old  type,  440-volt 
side  used  as  primary. 

Data 

Hysteresis  loop  and  magnetization  curve  are  given  in 
Fig.  14. 

Normal  eff.  e.  m.  f.  =  440  volts. 

Resistance  of  transformer  (440  volt-winding)  =  .26 
ohms. 

Maximum  value  of  normal  exciting  current  =  .655 
amp. 

From  Fig.  14 

5max  —  33-0  X  A\ 

Normal  residual  magnetism  =  28.0  K1 

£max  =  -y/2  X  440  =  622.5  VoltS. 

Equation  (8)  becomes 

A  B  =  —  33  Kl  A  (cos  B)  —  .0024  Kr  i 
From  Table  4,  Columns  16-19,  tne  maximum  current  is  62  amp.  or 
about  2.6  times  normal  full  load  current,  viz.,  -yj 2  X  17  =  24.1  amp. 
Transformer  E 

440,  220/220,  1 10  volts,  60  cycles,  new  type,  440-volt 
side  used  as  primary. 

Data 

Hysteresis  loop  and  magnetization  curve  are  given  in 
F'g-  IS- 

Normal  eff.  e.  m.  f .  =  440  volts. 

Resistance  of  transformer  (440-volt  winding)  =  .195 
ohms. 

Maximum  value  of  normal  exciting  current  =  .87  amp. 

From  Fig.  15 

5max  =38.0^3 

Normal  residual  magnetism  =  25.0  K 3 
£max  =tJz  X  440  =  622.5  volts 


YK.NSK.N — starting  itkrknts  ok  transform  i:ks 


33 


Equation  (8)  becomes 

A  B  =  —  38.0  Kj  A  (cos  6)  —  .002 1  KJ 
From  Table  4,  Columns  20-23,  the  maximum  current  is  255  amp.  or 
5.3  times  the  maximum  value  of  the  normal  full  load  current,  viz., 

-^2  X  34- 1  =  48-2  amp. 


34  ILLINOIS  ENGINEERING  EXPERIMENT  STATION 

IV.    Effect  of  Resistance  and  Inductance  in  Series  with 
Transformer  Primary. 


In  the  preceding  section,  have  been  presented  the  results  of  con- 
necting some  transformers  directly  to  the  busbars  with  negligible 
resistance  in  the  leads.  It  was  shown  that  with  the  old  type  of  trans- 
formers, the  initial  rush  of  current  may  amount  to  two  to  four  times 
normal  full  load  current,  while  with  the  new  type,  with  silicon  steel 
cores,  the  initial  rush  may  exceed  seven  times  full  load  current. 

The  only  remedy  for  reducing  these  abnormal  currents,  where  the 
transformer  is  to  be  connected  to  constant  potential  busbars,  is  the 
introduction  of  resistance  or  inductance  in  series  with  the  primary 
winding,  i.  e.,  that  side  of  the  transformer  which  is  to  be  connected  to 


 1  rWA/WVV 


 T 


Transformer 


Fig.  i  6. 


the  power  station.    This  inductance  or  resistance  will  take  care  of  a 
part  of  the  impressed  e.  m.  f.,  leaving  only  a  fraction  of  it  to  be  taken 
care  of  by  the  counter  e.  m.  f.  of  the  transformer.    This  is  shown 
diagrammatically  in  Fig.  16.    The  general  equation  then  is 
-       .    .       .  dB      ,_  di  , 

E™Sm6  =  Ad6  +X,d8  +Rl  (I0> 
which,  if  solved  for  A  B  in  the  same  way  as  in  Part  I,  gives 

A£  =  -l?maxA(cos0)-^  X    (At)-^^(A(9)    (ii) 

This  reduces  to  (8)  if  Xh  is  negligible. 

R  is  the  total  resistance  of  the  circuit,  including  the  transformer  pri- 
mary, and  ZL  is  the  inductive  reactance  outside  the  transformer. 

In  the  following,  will  be  calculated  the  maximum  rush  of  current 
with  either  resistance  or  inductance  in  series  with  the  transformer 
primary  for  two  of  the  silicon  steel  transformers,  transformer  A  and 
transformer  C. 

Transformer  A. 

Case  i. — For  negligible  inductance  outside  the  transformer  equa- 
tion (n)  becomes 


Y  K  X  S  !■'.  X  — ST  A  RT  IXC.  (IRK  K  N  TS  O  I'  IRA  X  SIORM  !•:  RS 


35 


 Bnvxx  A  (cos  6)  — ^x   Ri  (A  6) 

urn 

Suppose  now  that  A' =  1.211  ohms,  i.  e.,  that  the  outside  resistance  is 
1.21  —  .025=1.185  ohms,  since  the  resistance  of  the  transformer 
primary  is  .025  ohms.    For  io°  intervals  of  0,  A  0  =  .175. 

5max  =  29.5  K 

^m,x  =  155  VOltS 

R  =  1. 2 1  ohms 
A  B  =  —  29.5  K  A  (cos  0)  —  .0403  K  i. 

Case  2. — For  negligihle  resistance  in  the  leads,  the  total  resistance 
of  the  circuit  may  be  neglected,  and  (n)  becomes 

A5  =  -5maxA(cos0)-|^  Xt  (A  i) 

max 

Assume  XL  =1.21  ohms 

A  B  =  —  29.5  K  A  (cos  6)  —  .23  K  (At) 

Table  5  gives  the  calculations  for  these  and  the  following  cases.  It 
is  seen  from  this  table  that  the  maximum  rush  of  current  for  Case  1 
is  78.0  amp.,  and  for  the  second  case  86.0  amp.  or  less  than  twice  full 
load  current. 
Transformer  C. 

Case  1 — Negligible  inductance  outside  transformer. 

„      _      V2  normal  voltage      11 00 

For  R  =  '       —  5_  _  =  43  c  ohms 

full  load  current  24 

or  43.5  —  .5  =  43  ohms  in  series  with  the  2200-volt  winding,  equation 

(11)  reduces  to 

A  B  =  —  20.75  Kz  A  (cos  #)  —  -°5l  K2  i. 

Case  2. — Negligible  resistance  outside  transformer. 
For  Xh  =43.5  ohms  in  series  with  the  2200  volt-winding,  equation 
(11)  becomes,  neglecting  resistance : 

A5  =  —  20.75  K2  A  (cos  6)  —  .29  K2  (At). 
From  Table  5,  Columns  12-14,  it  may  be  seen  that  the  maximum  rush 
of  current  for  Case  1  is  50.0  amp.,  and  for  Case  2,  55  amp.,  i.  e.,  in  both 
cases  less  than  twice  full  load  current. 

From  the  above  calculations,  it  may  be  seen  that  the  initial  rush  of 
current  upon  closing  the  primary  circuit  of  a  transformer  can  be  lim- 
ited to  safe  values  by  inserting  either  a  resistance  or  an  air  core  in- 
ductance in  series  with  the  primary  circuit.  In  the  particular  cases 
above,  the  current  was  limited  to  less  than  twice  full  load  current  by 


JThis  resistance  multiplied  by  full  load  current,  45.5,  gives  a  drop  equal  to 
half  normal  voltage:  1.21X45.5  =  55  volts. 


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ILLINOIS  ENGINEERING  EXPERIMENT  STATION 


inserting  a  resistance  or  inductive  reactance  equal  to 

g  ^       y2  normal  voltage 

i- ~     full  load  current 

in  series  with  the  primary.1 

V.   Summary  and  Conclusions 

Table  6  gives  the  results  of  the  calculations  of  the  previous  sec- 
tions. Columns  9  and  10  give  the  results  for  the  case  in  which  the 
transformers  are  connected  to  the  busbars  with  sufficient  power  behind 
to  keep  the  voltage  constant  and  with  negligible  resistance  and  induct- 
ance in  the  leads.  Columns  11  and  12  give  the  results  for  the  same 
conditions,  but  with  a  resistance  of 

•'full  load 

in  series  with  the  primary. 

Columns  13  and  14  give  the  results  for  the  same  conditions  but 
with  a  reactance 

1  ful  1  load 

in  series  with  the  primary. 

Transformers  A,  C,  and  E  are  of  recent  manufacture  with  silicon 
steel  cores,  while  B  and  D  are  of  an  old  type. 

In  the  preceding  sections,  it  has  been  shown  that  transient  currents 
amounting  to  several  times  the  maximum  value  of  full  load  current 
may  occur  upon  closing  the  primary  circuit  of  a  transformer.  While 
this  transient  current  for  the  old  type  transformers  may  amount  to  two 
to  four  times  full  load  current,  it  may  rise  above  seven  times  the  maxi- 
mum value  of  full  load  current  for  transformers  with  cores  made 
from  silicon  steels  with  high  flux  densities- 

This  transient  current  becomes  a  serious  problem  only  for  sta- 
tions containing  step-up  transformers,  that  are  connected  directly  to 
the  station  busbars  through  leads  of  negligible  resistance  and  induct- 
ance. If  the  generators  are  belted  and  of  only  moderate  capacity,  the 
system  may  be  flexible  enough  to  stand  the  shock  due  to  the  enormous 
current  that  may  follow  upon  closing  the  transformer  switches.  If, 
however,  the  generators  are  of  large  capacity  and  direct-connected,  the 
shock  may  be  sufficient  to  cause  a  rupture  between  the  generator  and 
the  prime  mover.  It  will  readily  be  seen  that  this  current  will  be  of 
the  same  order  as  a  direct  short-circuit  current  of  the  generator. 

'For  calculations  of  inductance  coils  for  this  purpose  reference  is  made  to 
University  of  Illinois  Bulletin  53,  by  Prof.  Morgan  Brooks  and  Mr.  H.  M. 
Turner,  entitled,  "Inductance  of  Coils". 


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40 


ILLINOIS   K  NO  IN  KICK  INC   L'XI'KUI  M  KNT  STATION 


If  each  set  of  transformers  be  connected  to  one  generator,  the 
problem  will  consist  simply  in  bringing  the  voltage  up  slowly  with  the 
transformers  connected,  but  in  cases  where  it  becomes  necessary  to 
connect  transformers  to  busbars  of  full  potential,  it  becomes  necessary, 
for  safe  operation,  to  insert  in  the  primary  circuit  a  resistance  or  in- 
ductance to  limit  the  transient  current  to  safe  values.  It  has  been 
shown  that  a  resistance  or  inductive  reactance  amounting  to 

l/2  normal  voltage 
full  load  current 

will  limit  the  current  to  less  than  twice  full  load  current  under  the 
most  critical  conditions. 

This  resistance  or  inductance  needs  to  be  in  the  circuit  for  only 
a  very  short  time,  since  the  current  will  fall  down  to  below  full  load 


Transformer 


Fig.  17 


current  after  a  few  cycles.  The  resistance  or  inductance  may  be  con- 
nected as  shown  diagramatically  in  Fig.  17,  where  an  extra  contact,  A, 
is  provided  on  the  switch,  in  such  a  way  that,  in  closing  the  switch  the 
contact  A  is  reached  before  the  main  contact  B  is  reached.  It  might 
be  possible  to  provide  such  a  contact  even  on  oil  switches.  As  the  in- 
terval between  the  time  the  switch  touches  A  until  it  touches  B,  need 
be  only  a  fraction  of  one  second,  no  change  in  the  operating  mechanism 
of  the  switch  would  be  necessary.  Usually,  it  takes  an  oil  switch  about 
0.5  second  to  close,  i.  e.,  from  the  time  it  starts  until  the  switch  is  closed. 
If  the  contact  A  is  located  1/3  of  the  way  from  the  closed  position,  it 
may  take  the  contact  0.1  second  to  travel  from  A  to  B,  and  this  time 
will  be  sufficient  even  for  25  cycle  systems. 


\  ENSEN 


— START  I. \(,  l"  I' RUE  NTS  OF  TRANSFORM  ICRS 


41 


Appendix 

Residual  Magnetism. — It  has  been  generally  believed  that  residual 
magnetism  is  of  a  transient  nature,  i.  e.,  that  the  magnetism  that  re- 
mains in  the  iron,  after  removing  the  magnetizing  force,  gradually 
decreases. 

As  this  point  is  very  important  in  connection  with  the  starting 
current  of  transformers,  an  experiment  was  undertaken  to  ascertain 
whether  the  residual  magnetism  is  a  permanent  quantity  or  not.  Con- 
nections were  made  as  shown  in  Fig.  18. 


Fu;.  i  8 


Referring  to  the  hysteresis  loop  of  Fig.  3,  it  may  be  seen  that, 
starting  at  1,  opening  the  circuit  produces  a  change  of  flux  correspond- 
ing to  1-2;  reversing  the  current  produces  a  change  2-3,  etc.  However, 
if  the  residual  magnetism  at  2  decreases  before  the  current  is  reversed, 
the  change  of  flux  will  be  less  than  2-3.  Consequently,  the  problem 
consists  in  determining  whether  this  change  varies  with  the  time  elaps- 
ing between  opening  the  circuit  and  closing  it  again  in  the  opposite 
direction. 

The  time  interval  was  controlled  by  means  of  a  pendulum  and  four 
contacts,  A,  B,  C  and  D.  By  tracing  out  the  connections  in  Fig.  18,  it 
will  be  seen  that  with  all  the  levers  in  the  upright  position,  the  current 
flows  through  the  circuit  in  the  direction  of  the  arrows,  while  the 
galvanometer  G  is  shortcircuited  by  means  of  contact  B.  If  now  the 
pendulum  is  started  from  the  position  shov/n,  lever  A  is  first  knocked 
down  opening  the  primary  circuit.  The  change  of  flux  1-2  does  not 
produce  any  deflection  of  the  galvanometer,  because  it  is  shortcircuited 
until  lever  B  is  knocked  down.    Finally,  C  and  D  are  knocked  down, 


4-' 


ILLINOIS   KMILM-KKIM,    I'.X  l'l'.K  I  M  I'.N  T  STATION 


reversing  the  current,  producing  a  change  of  flux  2-3,  and  since  the 
galvanometer  is  no  longer  shortcircuited,  this  change  produces  a  de- 
flection of  the  galvanometer,  proportional  to  the  change  of  flux. 

The  shortest  distance  between  A  and  D  corresponded  to  about  .1 
second,  and  it  could  be  increased  to  about  y2  second. 

The  transformer  used  was  the  5-kw.  2080,  1040/460, 230  volt, 
60-cycle  transformer,  designated  as  transformer  B.  A  resistance  Rv, 
of  400  ohms,  was  inserted  in  the  primary  to  decrease  the  time  constant, 
and  the  current  was  maintained  at  the  maximum  value  of  the  normal 
magnetizing  current,  namely,  .1  amp. 

1.  The  deflection  corresponding  to  change  2-3  and  .1  second 
interval  between  A  and  D  was  48.0  cm.  The  interval  was  then  in  turn 
increased  to  Yz  second,  and  by  hand  operation  to  1  min.,  5  min.,  90  min., 
12  hrs.,  and  24  hrs. 

The  deflection  corresponding  to  the  change  2-3  was  in  every  case 
the  same. 

2.  To  ascertain  whether  there  was  any  decrease  of  flux  during 
the  .1  second  period,  the  resistance  Rg  amounting  to  more  than  1 
megohm  was  cut  out.  The  sensitiveness  of  the  galvanometer  is  such 
that  io~8  amp.  corresponds  to  1  mm.  deflection.  The  transformer  core 
has  a  cross-section  of  about  4  sq.  in.  and  the  number  of  turns  of  the 
230-volt  winding  is  80.  The  normal  flux  density  is  about  50  000  lines 
per  sq.  in.,  and  the  resistance  of  the  galvanometer  circuit  was  less  than 
1000  ohms.  Hence  to  produce  a  deflection  of  one  cm.  required  iO'T 
amp,  or  io-7  X  io3=  io-4  volts. 

IO8 

IO~4  IO8  IO4 

<f>  =  —  =  - —  =  12s  lines  per  sec. 

80  80 

That  is,  it  requires  a  change  of  flux  of  125  lines  per  sec.  to  produce  a 
large  deflection  of  the  galvanometer.  As  the  total  normal  flux  is 
50000  X  4  =  200000  lines,  this  is  less  than  1/10  per  cent,  so  that  any 
material  change  of  flux  occurring  within  the  first  1/10  sec.  after  open- 
ing A  would  be  recorded.  The  time  elapsing  between  A  and  B  was  less 
than  .01  sec.  The  pendulum  was  stopped  after  knocking  down  B,.  so 
that  any  deflection  occurring  after  the  change  1-2  would  be  due  to  the 
decrease  of  the  residual  magnetism. 

As  a  result  of  the  several  trials,  not  the  slightest  deflection  could 
be  detected. 

3.  It  was  finally  attempted  to  determine  the  effect  of  vibration 
and  blows  upon  the  permanency  of  the  residual  magnetism.  With  the 
same  connections  as  in  2,  A  and  B  were  knocked  down.    The  trans- 


V KNSKN 


— STARTING  ITKRKNTS  ()!•'  TRANSKORM  ICRS 


43 


former  core  was  then  given  a  series  of  blows  with  a  hammer.  The 
first  blow  produced  a  deflection  of  about  50  cm.,  and  the  successive 
blows  produced  deflections  decreasing  very  rapidly.  This  deflection 
corresponds  to  about  50/1000  =  .05  cm.  with  the  resistance  Rg  in 
circuit. 

Change  1-2  produced  a  deflection  of  8.5  cm. 
Change  2-3  produced  a  deflection  of  48.0  cm. 
Total  change  =  56-5  cm- 

This  means  that  the  maximum  value  of  the  normal  flux  corresponds 
to  28.3  centimeters  deflection,  and  the  residual  magnetism  to  28.3 
—  8.5  =  19.8  cm.  deflection.  Consequently,  a  deflection  of  .05  cm. 
corresponds  to  a  decrease  of  residual  magnetism  due  to  severe  blows 
of  5/20  per  cent  =1/4  per  cent. 

The  transformer  was  finally  given  continuous  hard  blows  for  5 
minutes  (one  blow  every  other  second)  after  point  2  had  been  reached. 
With  the  resistance  Rg  cut  out,  the  effect  of  the  last  blows  could  hardly 
be  noticed.  Rg  was  then  replaced  in  the  circuit  and  the  deflection  cor- 
responding to  the  change  2-3  was  observed.  The  result  showed  that 
the  effect  of  the  above  severe  treatment  was  to  decrease  the  residual 
magnetism  by  4  per  cent. 

Conclusion. — From  the  above,  the  conclusion  seems  justified  that 
there  is  no  decrease  in  the  residual  magnetism  of  a  transformer  under 
normal  conditions,  and  that  the  decrease  due  to  vibration  and  ordinary 
shocks  is  negligible. 


^^^^^^^^^^^^^^^^ 


arc*        -V  ./r^-jr*  /■ 


538 


aw 


.  <5frf  "T 


i^itf?  ^^***  <^4tc7 


UNIVERSITY  OF  ILLINOIS-URBAN  A 


3  0112  086829667 


